Xjyuk

Here is the problem, according to me:

In a classic hamburger, according to my internet research, approximately 906 kJ are contained.

Now take a car of 1 000 kilograms, and push it to 30 m/s. It has a certain kinetic energy, which is:
1 000 * 30² = 900 kJ

So does it mean that the work (in a physical sense) needed to stop the car is equivalent to the energy brought by the hamburger, so a human just have to eat an hamburger to be able to stop the car?

It is very hard to imagine, as even with the strength of an human and the possibility to brake the car very slowly, I think a human will need a lot of energy.

So how it is possible to compare the energy brought by food and the mechanical/kinetic energy?

Because on the other hand, it could also mean that with the energy brought by one hamburger (approximately 15% of the food energy is used by the human body, and the value I gave take into account this 85% factor), I am able to put push a car to 30 m/s!

There's something you're overlooking that makes the whole thing somewhat counter-intuitive: the maximum force the human can exert on the car.

In order to reach the kinetic energy of $450mathrmkJ$ that same amount of work $W$ has to be done on the car by the human, according to:

$$W=K$$

where:

$$mathbfdW=Fmathbfdx$$

Here $F$ is the force exerted by the human (we'll assume it constant, for simplicity's sake) and $mathbfdx$ the displacement (considered linear, for simplicity's sake). Integrating we get:

$$W=FDelta x$$

and:

$$FDelta x=frac12 mv^2$$

Or:

$$Delta x=fracm v^22F$$

Obviously if $F$ is relatively small compared to $mv^2$, $Delta x$ will be large. However that doesn't mean the human won't get the car up to speed: it just takes quite a long time.

It's similar if we made the car tow a fully loaded $20$ tonnes HGV: the car can do it but it would take an impractical amount of time because the maximum amount of force it can deliver is small compared to that of an HGV tractor.

It isn't so far fetched as it might appear. A gallon of gas will accelerate the car to speed and keep it there for perhaps 30 miles. The energy in gas comes from chemical bonds. The bonds in gas are not totally different from the bonds in a hamburger.

Burning a gallon of gas produces 132,000 BTU, or $1.39 times 10^8$ J. That is ~150 times more than the 900,000 J from burning a hamburger. Given the relative sizes, it sounds like gas has more energy per pound. So a hamburger has enough energy to run a car for about 0.2 miles.

Eating a hamburger for lunch produces enough energy to run a human until dinner. Over the course of an afternoon, a human could do enough work to push the car up to speed. Perhaps he could pedal a bicycle connected to a generator, and store the energy in batteries. Then the batteries might well have enough charge to get an electric car up to speed.

The whole scenario seems to be implausible when you consider that in order for the person to accelerate the vehicle to a speed of 30 m/s at the end the person would have to run at a pace of 70 mph!

As to the food calories burned:

According to one site an average person's straight pushing force is 60-80 N. Assuming 80 N and a 1000 kg car (2200 lb), which is a fairly light compared to the average, and negligible friction between the car and road, the car's acceleration would be 0.08$fracms^2$. That means it would take 6.26 minutes to reach 30 m/s and do 450 kJ of mechanical work.

Another site mentioned that human energy efficiency in converting food energy into mechanical output is about 25%. So the required food energy would be 450/.25, or 1800 kJ.

Hope this helps.

A calorimeter is a device that you can use to measure energy of food, You put a small amount of the food in a calorimeter. Then you submerge the calorimeter in a known quantity of water. Now you vaporize the food and measure the increase in temperature of the water. By careful measurements one can determine the energy required to heat the water. That amount of heat is the caloric content of that food.

Once you know the energy of the food you can compare it to other material objects just by calculating the energy of the objects. Kinetic energy is just $$(1/2) mv^2$$